Hemodiafiltration is a combined process in which hemodialysis and hemofiltration are carried out simultaneously. This process unites the advantages associated with convective mass transfer in hemofiltration and those of the dialytic diffusion process. To implement volumetric fluid balancing in known on-line hemodiafiltration processes, balancing chambers are utilized to directly measure a replacement fluid (substituate). Thus, a patient's fluid intake and output is centrally controlled by means of the balancing chambers, while all added and withdrawn fluids are observed. Also in an on-line process, no additional reservoir is needed for the substituate, because it is produced concurrently. In the known process, the substituate is sterilized by filtration using an especially provided on-line hemodiafiltration filter, which is present in addition to the actual hemodiafiltration filter. The additionally provided on-line hemodiafiltration filter is not replaced with every treatment. For that reason a separate contamination-prevention chamber is provided to reduce the risk of cross-contamination. In spite of this measure, there is still a residual risk of cross-contamination.